Question

Three numbers are in AP their sum is 24 and sum of their square is 200 find the numbers ​

Answer 1

Step-by-step explanation:

Given that :

Three numbers are in AP their sum is 24

In A.P any three numbers can be denoted as

→ a-d , a , a+d

here, a is the first term and d is its common difference.

a-d + a + a+d = 24

3a = 24

a = 24/3

a = 8 .........(i)

Now, We are given that sum of their square is 200

→ (a-d )²+ (a )² + ( a+d )² = 200

→ a² + d² -2ad + a² + a² +d² + 2ad = 200

→ 3a² + 2d² = 200

Put the value of a from (i)

→ 3(8)² + 2d² = 200

→ 3×64 + 2d² = 200

→ 2d² = 200 - 192

→ d² = 8/2

→ d² = 4

→ d = ± 2

So, we get A(first term) = 8 and common difference as ± 2

So the Numbers can be :

Taking D as positive

a-d , a , a+d $\implies$ 6 , 8 , 10

Taking D as negative

a-d , a , a+d $\implies$ 10 , 8 , 6

Finally , numbers are 6, 8, 10 but their order may depend on D.